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#' Titration Curve for a Weak Base
#'
#' This function calculates and plots the titration curve for a
#' monoprotic weak base analyte using a monoprotic strong acid as
#' the titrant. The calculation uses a single master equation
#' that finds the volume of titrant needed to achieve a fixed pH,
#' as outlined in R. de Levie's \emph{Principles of Quantitative
#' Chemical Analysis} (McGraw-Hill, 1997).
#'
#' @param conc.base Molar concentration of the weak base analyte;
#' defaults to 0.10 M.
#'
#' @param conc.acid Molar concentration of the strong acid titrant;
#' defaults to 0.10 M.
#'
#' @param pkw The pKw (or pKs) value for the solvent; defaults to water
#' as a solvent with a pKw of 14.
#'
#' @param pka The pKa value for the weak base analyte's conjugate weak
#' acid; defaults to a pKa of 9, or a pKb of 5 for the weak base analyte.
#'
#' @param vol.base Initial volume, in mL, of the solution that
#' contains the weak base analyte; defaults to 50.00 mL.
#'
#' @param plot Logical; if TRUE, plots the titration curve.
#'
#' @param eqpt Logical; if TRUE, draws a vertical line at the titration
#' curve's equivalence point.
#'
#' @param overlay Logical; if TRUE, adds the current titration curve
#' to the existing titration curve.
#'
#' @param \dots Additional arguments to pass to \code{plot()} function.
#'
#' @return A two-column data frame that contains the volume of titrant
#' in the first column and the solution's pH in the second column. Also
#' produces a plot of the titration curve with options to display the
#' equivalence point and to overlay titration curves.
#'
#' @author David T. Harvey, DePauw University. \email{harvey@@depauw.edu}
#'
#' @export
#'
#' @importFrom graphics plot lines
#'
#' @examples
#' ### Simple titration curve with equivalence point
#' ex4 = wb_sa(eqpt = TRUE)
#' head(ex4)
#'
#' ### Overlay titration curves using different pKa values
#' wb_sa(pka = 9, eqpt = TRUE)
#' wb_sa(pka = 7, overlay = TRUE)
#' wb_sa(pka = 5, overlay = TRUE)
#'
#' ### Overlay titration curve for strong base and weak base
#' sb_sa(eqpt = TRUE)
#' wb_sa(overlay = TRUE)
wb_sa = function(conc.acid = 0.1, conc.base = 0.1, pka = 9, pkw = 14,
vol.base = 50, plot = TRUE,
eqpt = FALSE, overlay = FALSE, ...) {
veq = conc.base * vol.base/conc.acid
ka = 10^-pka
kw = 10^-pkw
ph = seq(pkw, 1, -0.01)
h = 10^-ph
oh = kw/h
delta = h - oh
alpha = h/(ka + h)
volume = vol.base * (conc.base * alpha + delta)/(conc.acid - delta)
df = data.frame(volume, ph)
df = df[df$volume > 0 & df$volume < 2 * veq, ]
rownames(df) = 1:nrow(df)
if (plot == TRUE) {
if (overlay == FALSE) {
plot(df$volume, df$ph, type = "l", lwd = 2,
xlim = c(0, 1.5 * veq), ylim = c(0, pkw),
xlab = "volume of strong acid (mL)",
ylab = "pH", xaxs = "i", yaxs = "i", ...)
} else {
lines(df$volume, df$ph, type = "l", lwd = 2, ...)
}
if (eqpt == TRUE) {
x = c(veq, veq)
y = c(0, pkw + 1)
lines(x, y, type = "l", lty = 2, col = "red")
}
}
invisible(df)
}
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